Apparatus and process for the lateral deflection and separation of flowing particles by a static array of optical tweezers

ABSTRACT

A method and apparatus for laterally deflecting and/or separating a flow of particles using a static array of optical tweezers. In an array of optical tweezers with a lattice constant larger than the size of a particle of interest, particles driven past the array by an external force experience an additional interaction with the array of traps. By altering the angle of the array of traps relative to the external force, the particles&#39; movement from trap to trap inside the array can be biased away from the direction of the external force, thereby enabling selective deflection and/or separation of particles.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a Continuation of U.S. application Ser. No.09/951,117, filed Sep. 13, 2001, now U.S. Pat. No. 6,797,942incorporated herein by reference in its entirety.

This invention was made with U.S. Government support under Grant No.DMR-9730189 awarded by the National Science Foundation and through theMRSEC Program of the National Science Foundation under Grant NumberDMR-9880595. The Government has certain rights in this invention.

FIELD OF THE INVENTION

The present invention relates generally to a system and method forachieving a fractionation of particles. More particularly, the presentinvention relates to a system and method for achieving a lateralfractionation and/or separation of particles through the use of a staticarray of optical traps

BACKGROUND OF THE INVENTION

A number of techniques are conventionally known that are capable offractionating particles in limited circumstances. For example, one suchtechnique involves the use of a microfabricated sieve consisting of atwo-dimensional lattice of obstacles or barriers for DNA separation. Theasymmetric disposition of obstacles or barriers rectifies the Brownianmotion of DNA molecules that pass through the sieve, causing theparticles to follow paths that depend on the respective diffusioncoefficients of the DNA present. Although moderately effective, thistechnique includes a number of limitations. For example, because thelattice is microfabricated, the overall structure is capable of neithertuning nor adjusting the types and sizes of particles that arefractionated. Furthermore, such lattices tend to suffer from clogging,requiring flushing of the system and restarting.

Further, many conventional techniques for fractionating particlesachieve physical separation of the various fractions along the directionof an applied force. For this reason, they operate on discrete batchesof samples, and do not operate continuously.

SUMMARY OF THE INVENTION

It is therefore an object of the invention to provide an improved systemand method for the lateral deflection of flowing particles that is bothtunable and continuous.

It is another object of the invention to provide an improved system andmethod for laterally deflecting particles that does not become readilyclogged with particles.

It is still another object of the invention to provide an improvedsystem and method usable for particle purification and separation.

It is yet another object of the invention to provide an improved systemfor laterally deflecting particles that can be used for the purificationand separation of proteins.

It is another object of the invention to provide an improved system thatis capable of physically separating small particles by size, shape,dielectric constant, surface charge density, magnetic susceptibility,nonlinear optical properties, and index of refraction.

It is yet another object of the invention to provide an improved systemand method employing a minimal number of moving components for laterallydeflecting flowing particles.

It is still another object of the invention to provide an improvedsystem and method for laterally deflecting particles that is usable forthe separating of chromosomes.

It is yet another object of the invention to provide for an improvedsystem and method for laterally deflecting particles that can be usedfor DNA sizing.

It is another object of the invention to provide an improved system andmethod for laterally deflecting particles that can also be used topurify and/or separate macromolecules and/or nanoclusters or othernanosized material.

Further advantages and features of the present invention will beapparent from the following specification, claims and drawingsillustrating the preferred embodiments of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic of a holographic optical tweezer systemprojecting an optical tweezer array onto a flowing colloidal particlesuspension; FIG. 1B is a schematic view from the CCD camera of FIG. 1A;and FIG. 1C is a perspective representation of a 10×10 optical tweezerarray for laterally deflecting flowing particles in accordance with thepresent invention;

FIG. 2A is a plot showing the channeling of particles through analigned, 10×10 array of optical tweezers; FIG. 2B is a plot showing thetrajectories of particles flowing along the axes of a 10×10 array ofoptical traps oriented at a tilt angle of five degrees relative to theflow direction; FIG. 2C is a plot showing the trajectories of particlesthat are laterally deflected by a trap array oriented at a tilt angle ofthirty seven degrees with respect to the direction of flow; and FIG. 2Dis a plot showing the substantially undeflected trajectories ofparticles flowing past an array of traps oriented at a tilt angle offorty-five degrees with respect to the direction of flow;

FIG. 3 is a first representation of the movement of individual particlesthrough an array of optical traps offset from the direction of anexternal force by a tilt angle θ;

FIG. 4 is a second representation of the movement of individualparticles through an array of optical traps offset from the direction ofan external force;

FIG. 5 is a plot showing the ratio of transverse velocity to forwardvelocity of a particle relative to the angular orientation of the traparray for two different experimental runs under comparable conditions;and

FIG. 6 is a representation of a static array of optical tweezers used inconjunction with a microfluidics channel for particle separation.

DETAILED DESCRIPTION OF THE INVENTION

In order to illustrate embodiments of the invention, an explanation isprovided to describe the methodology and function of one embodiment ofthe present invention. Although the manner in which the phenomenon isdescribed is one rigorous approach which explains the operation of theinvention for those skilled in the art, other explanations also can beused to describe similar results which characterize embodiments of theinvention. The invention is therefore not limited to the description ofits operation by the following specification and drawings.

For a comprehensive understanding of the present invention, it ishelpful to consider a holographic optical tweezer system 10 as shown inFIG. 1A and a resulting square array 110 of individual optical tweezers112. The system 10 includes a laser beam 20 which is passed through adiffractive optical element 30, then processed by relay lens 40,reflected by dichroic mirror 50, and then laser beam 20 is focussed intooptical traps by objective lens 60. The optical traps (not shown) areformed in sample chamber 70 and the trapped particle array (not shown)is viewed by a conventional light microscopy system including condenserlens 80, the objective lens 60, a video eyepiece 85 and charge coupleddevice camera 90.

The resulting optical tweezer system 10 generates a square array 110 ofindividual optical tweezers 112 as shown in FIG. 1B. The opticaltweezers 112 exhibit a lattice constant which typically, although notexclusively, has a somewhat larger distance between the optical tweezers112 than the size of a particle 113 of interest. The particles 113driven past the array 110 by an external force from a bias source 117experience an additional interaction with the array 110 of individualtraps 112. If the trapping force is considerably greater than theexternal driving force, the particles 113 will become bound. If, on theother hand, the external force dominates, the particles 113 will flowpast the array 110 with their trajectories essentially unperturbed. Thepreferred embodiment operates in the intermediate regime in which theexternal force exceeds the trapping force for all of the particles 113in the sample, but to a differing degree for different fractions of thesample.

Under these conditions, the external force causes the particles 113 tohop from one of the traps 112 to another, occasionally pausing forperiods depending on the relative strengths of the optical traps 112 andexternal force, given the properties of the particular particle 113. Ifthe external force is aligned with the principal axes of the trappingarray 110, the resulting hopping trajectories will be aligned with theexternal force. If, on the other hand, the traps' axes are rotated withrespect to the direction of the external force, then the particles'hopping can be biased away from the direction of the external force.Such deflection has been shown in computer simulations of magnetic fluxquanta flowing through type-II superconductors and has been inferredindirectly from the appearance of transverse voltage gradients inperiodic Josephson junction arrays. The net deflection returns to zeroonce the array is rotated to 45° for one of two reasons (1) positive andnegative displacements can occur with equal probability or (2) theparticles jump diagonally through the array, having become locked intothe [11] direction.

FIGS. 3 and 4 are diagrammatic or illustrative general representationsof individual particles moving through the array 110 of the traps 112that has a tilt angle θ relative to the direction of an external biasforce 116 (see FIG. 1C also). As can be seen in FIGS. 3 and 4, dependingupon the relative tilt angle θ of the array 110, it is possible for theindividual particles 113 to be laterally deflected in both positive andnegative directions.

FIG. 2A shows an example of utilization of the system 10 withtrajectories 115 of 1.5 μm diameter silica, spherically shaped particles113 passing through the 10×10 array 110 of the optical traps or tweezers112, with about 2.4 μm of space between each of the tweezers 112. The“y” axis represents about 53 μm, and the “x” axis about 78 μm. In thisrepresentation, a pressure gradient is driving the particles 113 fromleft to right at a speed of about 30 μm/sec. With a substantially zerodegree tilt angle for the array 110, the particles 113 are locked into atrajectory (from left to right) with minimal lateral deflection. Themeasured particle trajectories shown in FIGS. 2A–2D are also orientedwith the applied flow directed from left to right.

FIG. 2A therefore shows trajectories of roughly 1000 spheres (theparticles 113) with the flow aligned along the [10] lattice direction.The particles 113 are drawn into the rows of the tweezers 112 from anarea extending to about 3 μm beyond the array's boundaries, andthereafter follow the [10] rows to their ends. Transverse fluctuationsare greatly suppressed by the trapping potential while the particles'longitudinal motion is punctuated only by brief irregular pauses inindividual optical potential wells. The time required for the particle113 to make a transverse jump is so much greater than the longitudinaljump interval that the particles 113 essentially never leave the [10]rows. This influence of the discrete trapping potential on theparticles' trajectories constitutes a kinetically locked-in state. Oncethe particles 113 have hopped through the ranks of the tweezers 112,they return to the bulk flow, their trajectories eventually blurringinto each other through diffusion.

Rotating the diffractive optical element 30 through an angle θ alsorotates the pattern of the tweezers 112 with respect to the flowdirection without otherwise altering the traps' characteristics. FIG. 2Bshows the same sample with the optical tweezers 112 oriented at θ=5°with respect to the flow. As in FIG. 2A, the particles' tracks remainclosely locked in to the array's [10] rows. Unlike the example in FIG.2A, however, the trajectories now are systematically deflected away fromthe flow's direction. This deflection leaves a distinct shadow on thedownstream side of the array into which comparatively few of theparticles 113 wander.

Further rotation changes the array's influence markedly. FIG. 2C showsthe array rotated to θ=37°, with other conditions unchanged. Rather thanfollowing the [10] lattice rows to positive deflection, the particles113 have now locked in to the [11] lattice direction and experience aretrograde deflection. This crossover from [10] to [11] locked-in statesreflects the different local potential energy landscape the particle 113experiences as it is forced along different directions. At somethreshold angle beyond the geometrically determined crossover point at22.5°, the jump rate for [11] hops exceeds that for [10] hops by a largeenough margin that the particles 113 become locked in to diagonaltrajectories. Rotating still further to θ=45° as in FIG. 2D reduces thedegree of deflection while enhancing the trajectories' alignment withthe [11] lattice direction.

It is believed that the kinetically locked-in states should form ahierarchy whose influence on transport properties is expected to takethe form of a Devil's staircase of plateaus in the longitudinaltransport with increasing rotation. Our observation of states lockedinto the [10] and [11] directions correspond to the principal plateausof these hierarchies.

We also observe the sign of the transverse deflection to change withmonotonically increasing rotation angle θ. This differs from othersystems in that no change of sign is predicted for the Hall coefficientof a periodically modulated two-dimensional electron gas with increasingmagnetic field. If indeed such sign reversal could be obtained throughsimple patterning of an electronic system, the effect would beadvantageous and could have widespread applications in magnetic dataretrieval.

FIG. 5, the data points and connecting solid lines represent therelative transverse velocity attained by the particles 113 when theapplied and trapping forces they experience in the system 10 arecomparably strong. The dashed line, on the other hand, represents theabsence of transverse deflection expected for the same particle 113 ifthe applied force 117 were to dominate the trapping force. FIG. 5 alsoshows that the amount and direction of lateral deflection can beoptimized by changing the rotation angle θ for a given laser power andthe external driving force 117. Reducing the laser power would reducethe maximum deflection attainable, with no deflection occurring when thelaser 20 is extinguished (See FIG. 1A). As can also be seen in FIG. 5,there is virtually no lateral deflection at all when the tilt angle is θeither 0° or about 22.5°, nor should there be a deflection for θ ofabout 45°. It should also be noted, however, that there is also nolateral deflection when the tilt angle is about 22.5°. Empirical datahas suggested that, for a given particle size and power level, themaximum amount of lateral deflection occurs when as the tilt angleapproaches about 17°. When the tilt angle passes about 22.5°, thelateral deflection of the particle 113 changes direction entirely.Empirical data has suggested that the maximum deflection in thisopposite direction occurs as the tilt angle approaches 30°, althoughthis maximum deflection is substantially smaller than the maximumdeflection which occurs at about 17°. The nonmonotonic dependence oflateral deflection on orientation is clearly resolved. Other possiblelock-in orientations at intermediate and smaller angles may be difficultto resolve in a system of the present size. In principle, transportthrough larger arrays of the optical tweezers 112 would reveal a moreextensive hierarchy of locked-in states, possibly resembling the Devil'sstaircases predicted for other systems.

As explained in more detail in the Example provided hereinafter, passiveoptically-induced lateral deflection in accordance with the presentinvention has been observed in a suspension of colloidal silica spheres1.5 μm in diameter dispersed in demonized water. A 10×10 array of theoptical tweezers 112 was created with a static computer-generateddiffraction grating illuminated by 73 m W of laser light at a wavelengthof 532 nm in a standard holographic optical tweezer (HOT) optical train.The particles 113 were contained between parallel glass walls in asealed sample chamber 70. Flow was induced with a pressure differentialacross the sample chamber 70. The particles' trajectories across the78×53 μm² field of view were recorded on video tape before beingdigitized and analyzed using conventionally-known image analysistechniques.

The laterally deflected particles 113 can be collected by a variety ofmethods according to the present invention. These methods include theuse of microfluidics channels. The particles 113 not deflected by thearray, presumably because they interact less strongly with the opticaltraps or more strongly with the external force, will not be deflectedand so will not be collected. This distinction makes possiblefractionation of the particles 113 based on quite general considerationsof their physical properties, with control parameters including scale,symmetry, extent, and intensity of the optical trapping arrays, and thenature and strength of the external force. In the example shown in FIGS.2A–2D, the external force was provided by hydrodynamic drag. Further,separation of particles can be effectuated on the basis of sensitivityto driving force, laser beam intensity, and optical gradient conditionswherein particle sensitive variables are particle size, particle shape,dielectric constant, surface change density, magnetic susceptibility,nonlinear optical properties and index of refraction.

Reducing the traps' efficacy either by reducing the laser intensity orelse by increasing the external driving force allows otherwise locked-inones of the particles 113 to cross more easily from one row of thetweezers 112 to the next. This reduces the degree of mode locking for agiven angle, and thus also the angle of maximum deflection and also themaximum deflection itself, until finally none remains. This thresholdshould be independent of the array's extent.

Loss of deflection upon depinning also provides the basis for a verygeneral continuous fractionation technique. The particles 113 morestrongly influenced by the array of the tweezers 112 could be deflectedto greater angles than the particles 113 driven more strongly by theexternal force. Consider, for example, colloidal spheres for theparticles 113 which differ only in their radii, a. The optical gradientforce exerted on sub-wavelength sized spheres varies roughly as a³. Thewell known Stokes drag, on the other hand, varies as “a”. Larger spheresembodying the particles 113, therefore, are disproportionatelyinfluenced by the optical tweezers 112, while the smaller particles 113can pass through with smaller deflection. Orienting the array 112 of theoptical tweezers 112 near the angle of optimal deflection and adjustingthe intensity to place the largest particles 113 in the hoppingcondition therefore deflects that largest fraction laterally out of theotherwise mixed flow. The deflected fraction can be collectedcontinuously, for instance by flowing the separated fractions intoseparate microfluidic channels. The undeflected fraction can be furtherfractionated by additional stages of the optical tweezers 112 downstreamof the first. These additional stages can even be integrated into asingle holographic optical tweezer array with gradated characteristics.

Continuous fractionation offers obvious benefits over traditionalmethods such as gel electrophoresis which separate a sample's fractionsalong the line of the applied force and thus can only operate on adiscrete amount of material at a time.

As described in the background, competition between misaligned forceshas been applied to other continuous fractionation schemes, includingelectrophoresis through arrays of microfabricated posts and flow pastdielectrophoretic Brownian ratchets created from asymmetricinterdigitated electrodes. Optical fractionation offers severaladvantages. The array of the optical tweezers 112 can be reconfigureddynamically by varying the laser intensity and array orientation. Eventhe lattice constant and symmetry can be adjusted to suit the separationproblem at hand. Unlike posts which present a fixed barrier to all theparticles 113, the optical tweezers 112 can have markedly differentinfluences on different materials. Choice of wavelength therefore opensup additional possibilities for continuous optical fractionation. All ofthese performance-determining properties, furthermore, can be variedcontinuously during operation. Common failure modes such as cloggingsimilarly can be remedied by extinguishing the trap array. Also unlikesystems based on microfabricated sample chambers, optical fractionationrequires quite simple sample handling, all of the sorting beingaccomplished by patterns of light rather than by distributions ofmatter. Recent observations of molecular drift mediated by opticalgradients allow one to conclude that fractionation based on transportthrough the arrays 110 of the optical tweezers 112 can apply even downto the scale of macromolecules. Straightforward consideration of theforces in the implementation of passive optically-induced lateraldeflection described herein demonstrate the ability of highly selectivefractionation.

The above described principles can be used as a method for separatingthe particles 113 into two different flow streams. FIG. 6 shows anexample of a microfluidics channel 120 that branches into a firstsubchannel 122 and a second subchannel 124. Before the division of themicrofluidics channel 120 into the first and second subchannels 122 and124, an array 126 of optical tweezers 128 is angularly offset relativeto the flow u from an external force. In the case where a largerparticle 130 and a smaller particle 132 both pass through the array 126,the larger particle 130 incurs more lateral deflection than the smallerparticle 132 due to the particle's larger radius. As a result of thisaction, the smaller particle 132 will travel in a substantially straightline into the second subchannel 124, while the larger particle 130 willtravel into the partially offset first subchannel 122.

The method of the invention can thus be used in a variety ofapplications. These applications include, without limitation, theseparation of chromosomes, the purification of particle types andproteins, and DNA sizing. Additionally, macromolecules and nanoclusterscan be manipulated in a similar manner. Furthermore, it is also possibleto incorporate a number of angularly offset arrays of the tweezers 112in series with each other. Such an arrangement allows for the furtherseparation of the particles 113.

The following non-limiting example illustrates generally certainprincipals of the invention.

EXAMPLE

One preferred system, shown schematically in FIG. 1 includes 1.5 μmdiameter silica spheres (Bangs Labs) dispersed in deionized water andconfined to a horizontal layer 15 μm thick between parallel glasssurfaces. These spheres are considerably denser than water and readilysediment into a monolayer about 2 μm above the lower wall of the samplecontainer. The edges of the sample volume are sealed to form a flowchannel. Two glass tubes bonded to holes through the upper glass wallprovide access to the sample volume and serve as reservoirs for colloid,water and clean mixed-bed ion exchange resin. The ends of the tubes areconnected to continuous flows of humidified Ar gas. Blocking one of theflows causes a pressure imbalance which drives colloid through thesample chamber and past the 75×58 μm² field of view of a 100×NA 1.4oil-immersion objective mounted on an Olympus IMT-2 microscope base. Bycontrolling the flow of Ar, we can induce colloid to travel at up to 100μm/sec over periods of an hour or more.

The individual spheres' in-plane motions are tracked with a resolutionof 10 nm at 1/60 sec intervals using precision digital video microscopy.The resulting trajectory data allow us to monitor the spheres' progressthrough potential energy landscapes that we create with light.

Our optical potential landscapes are based on the holographic opticaltweezer technique in which a single beam of light is formed intoarbitrary configurations of optical traps using a computer-generateddiffractive beam splitter. Each beam created by this diffractive opticalelement (DOE) is focused by the objective lens into adiffraction-limited spot capable of stably trapping one of the silicaspheres. While holographic optical tweezers can be arranged arbitrarilyin three dimensions, we chose a planar 10×10 square array with 2.4 μmlattice constants to model the free energy modulations typicallydiscussed in theoretical and numerical treatments of analagous physicalsystems. The traps are focused into the plane of the monolayer to avoiddisplacing spheres vertically as they flow past.

If the Stokes drag due to the flowing fluid greatly exceeds the opticaltweezers' maximum trapping force, then colloidal particles flow past thearray with their trajectories unperturbed. Conversely, if the trappingforce dominates, then particles fall irreversibly into the first trapsthey encounter. Our observations are made under intermediate conditionsfor which trapping and viscous forces are nearly matched. Under theseconditions, the trapping array's influence on a particle's trajectorydepends on its orientation with respect to the flow. Insymmetry-hindered directions for which the trapping force exceedsviscous drag, the flow still can push a particle far enough to the edgeof an individual trap that it can make a thermally-assisted jump to thenext well. Lower potential barriers in symmetry-favored directions mayonly modulate the speed of a passing particle. A particle hopping fromwell to well under these circumstances chooses a path through thepotential energy landscape based on a tradeoff between geometricproximity and energetic expediency. These tradeoffs lead to interestingkinetic transitions as the driving force's relationship to the trappingpotential changes.

Our silica spheres enter the hopping state for flow speeds of 30±3μm/sec and laser intensities of 100±10 μW/trap. The real density ofspheres in the minelayer is low enough that no more than 5% of the trapsare occupied at any time. While collisions sometimes occur betweenhopping particles, they are comparatively rare. The data shown in FIGS.2A–2D were obtained in this manner.

While preferred embodiments of the invention have been shown anddescribed, it will be clear to those skilled in the art that variouschanges and modifications can be made without departing from theinvention in its broader aspects.

1. An apparatus for controlled deflection of particles, comprising: aplurality of particles; an external bias force from a bias force sourceapplied to the plurality of particles; and an optical tweezer arrayhaving optical gradient forces associated therewith and the opticalarray oriented at a tilt angle relative to a direction of the bias forcegenerated by the bias force source whereby the optical gradient forcesof the optical tweezer array interact with the bias force to deflect theplurality of particles.
 2. The apparatus as defined in claim 1 whereinthe external bias force from the bias source and the optical tweezerarray and the associated optical gradient forces are adjustable to achange in amount and direction of deflection of selected ones of theplurality of particles.
 3. The apparatus as defined in claim 2 furtherincluding a diffractive optical element to generate the optical tweezerarray, the diffractive optical element rotated by an angle to rotate theoptical tweezer array with respect to flow direction of the plurality ofparticles, thereby enabling selected change of amount of deflection forthe particles.
 4. The apparatus as defined in claim 3 wherein thediffractive optical element is rotated to a particular range of angleswhich cause the plurality of particles to be deflected away fromdirection of flow of the particles.
 5. The apparatus as defined in claim3 wherein retrograde deflection with respect to the angle of rotation isachieved by means of generating a different local potential energylandscape of the optical tweezer array at selected angles of rotationfor the diffractive optical element.
 6. The apparatus as defined inclaim 5 wherein the different local potential energy landscape causesformation of threshold angles of rotation of the optical tweezer array,thereby achieving locked in trajectories of the particles.
 7. Theapparatus as defined in claim 6 wherein a hierarchy is established toprovide a form of Devil's staircase of plateaus in transverse transportof the particles with increasing angle of rotation of the diffractiveoptical element.
 8. The apparatus as defined in claim 2 whereintransverse deflection of the particles undergoes a change of sign withchanging the angle of rotation of the optical tweezer array.
 9. Theapparatus as defined in claim 1 achieves the plurality of particlescomprises different types of particles which respond differently to theoptical tweezer array and the external bias force, thereby enablingsorting of the different type of particles.
 10. The apparatus as definedin claim 1 wherein a continuous source of the plurality of particles isprovided and continuous fractionated portions are produced.
 11. Theapparatus as defined in claim 1 further including means to monitorclogging of the apparatus and to remedy clogging by extinguishing theoptical tweezer array.
 12. The apparatus as defined in claim 1 furtherincluding a plurality of microfluidic channels disposed to collect theindividual particle flow channels created by control of the opticalarray of the flow of particles created by the bias force from the biasforce source.